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A merchant has 3 kinds of wine. 403 gallons of first kind, 527 gallons

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Bunuel
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A merchant has 3 kinds of wine. 403 gallons of first kind, 527 gallons [#permalink] New post   25 Nov 2021, 10:00
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A merchant has 3 kinds of wine. 403 gallons of first kind, 527 gallons of second kind & 589 gallons of third kind. Find the least number of casks of equal size in which the wine can be stored without mixing.

(A) 49
(B) 31
(C) 19
(D) 17
(E) 13
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A merchant has 3 kinds of wine. 403 gallons of first kind, 527 gallons [#permalink] New post   25 Nov 2021, 10:36
For highest capacity container we need the H.C.F. of all amounts of the wine.

H.C.F. of 403, 527 and 589 = 31

Now the number of full casks required = \(\frac{403+527+589}{31}\) = 49 (A)
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Re: A merchant has 3 kinds of wine. 403 gallons of first kind, 527 gallons [#permalink] New post   25 Nov 2021, 10:58
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Technically the answer is 3, because you can just use three 600-gallon casks (or any other size 589 gallons or greater). If the casks need to be filled completely, then pyjamascientist's solution is perfect.
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Re: A merchant has 3 kinds of wine. 403 gallons of first kind, 527 gallons [#permalink] New post   27 Nov 2021, 10:16
IanStewart wrote:
Technically the answer is 3, because you can just use three 600-gallon casks (or any other size 589 gallons or greater). If the casks need to be filled completely, then pyjamascientist's solution is perfect.


I couldn't help but smile at the highlighted statement...but yes going by what the question maker is trying to mean, 49 is the correct answer as given by PyjamaScientist
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Re: A merchant has 3 kinds of wine. 403 gallons of first kind, 527 gallons [#permalink] New post   11 Sep 2023, 13:22
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Re: A merchant has 3 kinds of wine. 403 gallons of first kind, 527 gallons [#permalink]
11 Sep 2023, 13:22
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